New Analysis on Galerkin FEMs for Nonlinear Parabolic PDEs

Linearized (semi)-implicit schemes are the most commonly-used approximations in numerical solution of nonlinear parabolic equations since at each time step, the schemes only require the solution of a linear system. However the time step restriction condition of schemes is always a key issue in analysis and computation. For many nonlinear parabolic systems, error analysis of Galerkin type finite element methods with linearized semi-implicit schemes in the time direction is established usually under certain time step condition $\tau \le h^{\alpha}$ for some $\alpha>0$. Such a time-step condition may result in the use of a very small time step and extremely time-consuming in practical computations. The problem becomes more serious when a non-uniform mesh or adaptive meshing is used. In this talk, we introduce a new approach to unconditional error analysis of linearized semi-implicit Galerkin FEMs for a large class of nonlinear parabolic PDEs. ; Non UBC ; Unreviewed ; Author affiliation: City University of Hong Kong ; Faculty